Solve for $x$ and $y$ using elimination. ${2x+y = 6}$ ${-3x-y = -7}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $-x = -1$ $\dfrac{-x}{{-1}} = \dfrac{-1}{{-1}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {2x+y = 6}\thinspace$ to find $y$ ${2}{(1)}{ + y = 6}$ $2+y = 6$ $2{-2} + y = 6{-2}$ ${y = 4}$ You can also plug ${x = 1}$ into $\thinspace {-3x-y = -7}\thinspace$ and get the same answer for $y$ : ${-3}{(1)}{ - y = -7}$ ${y = 4}$